Render what camera sees and not first frame
No need to scrub every time from the beginning. You can adjust the range of frames to start rendering (and playing) from however you want. Look in the Properties Panel for the Output Settings tab, and adjust the range for the frames you want rendered. Your file is likely starting from the beginning because the start frame is 1 by default. Change this setting to something later in the timeline.

You can alternatively change this same range setting in the Timeline Editor window, which can be found at the bottom of the screen while using the Animation Workspace. Changing it in either location changes it in the other.